We obtain an analytical solution for two-dimensional steady-state transport of conservative contaminant between injecting and pumping wells. Flow and transport are considered in the vertical cross-section. The Dupuit approximation and conformal mapping onto the complex potential domain are employed to determine the velocity and concentration distributions, respectively. We use this solution to derive a priori conditions under which widely used 1-D analytical solutions with constant velocity and dispersion coefficients provide accurate approximations. These conditions are formulated in terms of aquifer parameters, such as hydraulic conductivity, porosity and dispersivities, and remediation strategy, e.g., well spacing and pumping regimes.